Geometric Structures: Problem Set B (Triangles in the Euclidean and Taxicab Planes)
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
1. Determine the Euclidean side lengths and the Taxicab side lengths of the triangles below.
a. C = (0, 0), B = (2, 0), A = (0, 2)
b. C = (0, 0), B = (-2, 0); A = (0, 2)
c. C = (0, 0), B = (-2, 0), A = (0 -2)
d. C = (2, 2), B = (-2, 0), A = (0, -2)
e. Which of the triangles, if any, are congruent to each other?
f. Which of the triangles, if any, are right triangles?
g. Which of the triangles, if any, are scalene triangles?
h. Which of the triangles, if any, are equilateral?
2. Can you find a Taxicab geometry triangle which is both equilateral and a right triangle?
3. In the Euclidean Plane two triangles are congruent if they obey a. SSS (Side, Side, Side), SAS (Side, Angle Side), or AAS (Angle, Angle Side). However, in the Euclidean Plane AAA and SSA do not guarantee congruence. Give examples to show this and give examples to show what happens in the Taxicab plane.